Achievements of Lobachevsky. Lobachevsky Nikolai Ivanovich: interesting data and facts

1792

Nikolai Ivanovich Lobachevsky (November 20 (December 1) 1792, Nizhny Novgorod - February 12 (24), 1856, Kazan), great Russian mathematician, creator of Lobachevsky's geometry, figure in university education and public education. The famous English mathematician William Clifford called Lobachevsky the “Copernicus of geometry.”

N. I. Lobachevsky was born in Nizhny Novgorod. His parents were Ivan Maksimovich Lobachevsky (an official in the geodetic department) and Praskovya Aleksandrovna Lobachevskaya. In 1800, after the death of her father, her mother and her family moved to Kazan.

To live means to feel, to enjoy life, to certainly feel something new that would remind us that we are living... Let us cherish life until it loses its dignity. Let examples in history, the true concept of honor, love for the fatherland, awakenings in in my youth, will give in advance...a noble direction to passions.
(from the article “On the most important subjects of education” July 5, 1828)

Lobachevsky Nikolai Ivanovich

There Lobachevsky graduated from the gymnasium (1802–1807), and then (1807–1811) from the newly founded Kazan Imperial University, to which he devoted 40 years of his life.

During his studies at the university, Lobachevsky was greatly influenced by Martin Fedorovich Bartels, a friend and teacher of the great German mathematician Carl Friedrich Gauss. He took patronage over a poor but gifted student.

In his senior year, Lobachevsky’s description included “dreamy self-conceit, perseverance, disobedience,” as well as “outrageous actions” and even “signs of godlessness.” The threat of expulsion hung over him, but the intercession of Bartels and other teachers helped avert the danger.

After graduating from the university, Lobachevsky received a master's degree in physics and mathematics with honors (1811) and was retained at the university. In 1814 he became an adjunct, 2 years later - extraordinary, and in 1822 - ordinary professor. Students highly appreciated Lobachevsky's lectures.

The range of his responsibilities was extensive - lecturing on mathematics, astronomy and physics, equipping and putting in order the library and museum, etc. The list of official duties even includes “monitoring the reliability” of all students in Kazan.

In 1819, an auditor (M. L. Magnitsky) came to Kazan, who gave an extremely negative opinion on the state of affairs at the university. Magnitsky was appointed trustee; he fired 9 professors, introduced strict censorship of lectures and a barracks regime. Bartels left for Dorpat, and Lobachevsky was appointed dean of the Faculty of Physics and Mathematics.

During these years he wrote textbooks on geometry and algebra; the first of them was condemned for using the metric system of measures, and the second was not printed at all.

In 1826, Magnitsky was removed from the post of trustee for abuses. A new trustee is appointed (M. N. Musin-Pushkin). Lobachevsky is elected rector of the university.

He plunges headlong into economic affairs - reorganizing the staff, building mechanical workshops, laboratories and an observatory, maintaining a library and mineralogical collection, participates in the publication of the Kazan Bulletin, etc.

He does a lot with my own hands. Gives popular science lectures on physics to the public. And at the same time, he tirelessly develops and polishes his life’s work - non-Euclidean geometry.

In 1832, Lobachevsky married Varvara Alekseevna Moiseeva. They had seven children.
1834: instead of the Kazan Bulletin, the publication of Scientific Notes of the Kazan University begins.

Lobachevsky was the rector of Kazan University from 1827 to 1846, surviving a cholera epidemic (1830) and a severe fire (1842) that destroyed half of Kazan.

Thanks to the energy and skillful actions of the rector, casualties and losses in both cases were minimal. Through the efforts of Lobachevsky, Kazan University is becoming a first-class, authoritative and well-equipped educational institution, one of the best in Russia.

On November 20, 1845, Lobachevsky was confirmed for the sixth time as rector for the new four-year period. Despite this, in 1846 the Ministry rudely removed Lobachevsky from the post of rector and professorial chair (officially due to deteriorating health).

Formally, he even received a promotion - he was appointed assistant trustee, but he was not given a salary for this work.

Soon Lobachevsky was ruined, his wife’s estate was sold for debts. In 1852, Lobachevsky's eldest son died. His health has deteriorated and his eyesight is weakening. Main work scientist, “Pangeometry” was taken from dictation by the students of a blind scientist in 1855.

He was buried at the Arskoye cemetery in Kazan.

In 1892, Lobachevsky’s 100th anniversary was widely celebrated in Russia and other countries. An international prize was established (Lobachevsky Medal, 1895), and a monument to the scientist was unveiled in Kazan (1896).

The 200th anniversary of Lobachevsky was celebrated in 1992. The Bank of Russia issued commemorative coin in the series “Outstanding Personalities of Russia”.

A crater on the Moon is named after Lobachevsky. Streets in Moscow and Kazan also bear his name. scientific library Kazan University. On March 20, 1956, a decree was issued by the Presidium of the Supreme Soviet of the USSR on naming Gorky (Nizhny Novgorod) University named after N. I. Lobachevsky.

Student notes of Lobachevsky's lectures (from 1817) have been preserved, where he attempted to prove Euclid's fifth postulate, but in the manuscript of the textbook “Geometry” (1823) he already abandoned this attempt.

In “Reviews of the Teaching of Pure Mathematics” for 1822/23 and 1824/25, Lobachevsky pointed out the “still invincible” difficulty of the problem of parallelism and the need to accept in geometry as initial concepts directly acquired from nature.

On February 7, 1826, Lobachevsky submitted an essay for publication in the Notes of the Physics and Mathematics Department: “ Concise presentation began geometry with a rigorous proof of the parallel theorem" (in French). But the publication did not materialize.

The manuscript and reviews have not survived, but the essay itself was included by Lobachevsky in his work “On the Principles of Geometry” (1829–1830), published in the magazine “Kazansky Vestnik”. This work became the first serious publication in world literature on non-Euclidean geometry, or Lobachevsky geometry.

Lobachevsky considers Euclid's parallelism axiom to be an arbitrary restriction. From his point of view, this requirement is too stringent, limiting the possibilities of the theory describing the properties of space.

As an alternative, he proposes another axiom: on a plane, through a point not lying on a given line, there passes more than one line that does not intersect the given one.

The new geometry developed by Lobachevsky does not include Euclidean geometry, however, Euclidean geometry can be obtained from it by passing to the limit (as the curvature of space tends to zero). In Lobachevsky geometry itself, the curvature is negative.

However, Lobachevsky's scientific ideas were not understood by his contemporaries. His work “On the Principles of Geometry,” presented in 1832 by the university council to the Academy of Sciences, received a negative assessment from M. V. Ostrogradsky. Among his colleagues, almost no one supports him, misunderstanding and ignorant ridicule are growing.

The culmination of the persecution was a mocking anonymous libel that appeared in F. Bulgarin’s magazine “Son of the Fatherland” in 1834:

How can one think that Mr. Lobachevsky, an ordinary professor of mathematics, would write a book for some serious purpose that would bring a little honor to the latter? school teacher? If not scholarship, then at least common sense every teacher should have, and in new geometry this latter is often lacking.

But Lobachevsky does not give up. In 1835–1838, he published articles on “imaginary geometry” in Scientific Notes, and then the most complete of his works, “New Principles of Geometry with the Complete Theory of Parallel,” was published.

Not finding understanding at home, he tries to find like-minded people abroad. In 1840, Lobachevsky published “Geometric Studies on the Theory of Parallel” in German, which contains a clear statement of his main ideas. One copy is received by Gauss, the “king of mathematicians” of that time.

As it turned out much later, Gauss himself secretly developed non-Euclidean geometry, but never decided to publish anything on this topic.

Having familiarized himself with Lobachevsky's results, he expressed his sympathy for the ideas of the Russian scientist indirectly: he recommended electing Lobachevsky as a foreign corresponding member of the Royal Society of Göttingen. Gauss entrusted rave reviews about Lobachevsky only to his diaries and closest friends.

This election took place in 1842. However, it did not strengthen Lobachevsky’s position. He still has four years left to work at his native university.

Lobachevsky was not the only researcher in this new field of mathematics. The Hungarian mathematician Janos Bolyai, independently of Lobachevsky, published his description of non-Euclidean geometry in 1832. But his works remained unappreciated by his contemporaries.
Jubilee Medal 1895

Lobachevsky died unrecognized. Several decades later, the situation in science has changed radically. The studies of E. Beltrami (1868), F. Klein (1871), A. Poincaré (1883) and others played a major role in the recognition of Lobachevsky’s works.

The appearance of the Klein model proved that Lobachevsky geometry is as consistent as Euclidean geometry. The realization that Euclidean geometry had a viable alternative made a huge impression on the scientific world and gave impetus to other innovative ideas in mathematics and physics.

Lobachevsky obtained a number of valuable results in other branches of mathematics: for example, in algebra he developed new method approximate solution of equations, in mathematical analysis he obtained a number of subtle theorems about trigonometric series, clarified the concept of a continuous function, etc.

In the 1950s, American satirist, singer and mathematician Tom Lehrer wrote a satirical song dedicated to Lobachevsky, which was popular in intellectual circles in the United States.

In this song, he introduces Lobachevsky as his teacher, who taught him plagiarism. It is worth noting that Lobachevsky was included in this song mainly because his last name was close in sound to the hero of the song parodied by Lehrer - Stanislavsky.

In Poul Anderson's science fiction novel Operation Chaos, Lobachevsky's ghost was summoned by the heroes to help them make measurements that obey the laws of non-Euclidean geometry.

N. I. Lobachevsky. Complete works in five volumes. M.: GITTL.

Volume 1, 1946.
*Geometric research on theory parallel lines.
*On the principles of geometry.

Volume 2, 1949.
*Geometry. New principles of geometry with a complete theory of parallels.

Volume 3, 1951.
*Imaginary geometry.
*Application of imaginary geometry to some integrals.
*Pangeometry.

Volumes 4–5, 1951.
*Works in other fields, letters.

N. I. Lobachevsky. Geometric studies on the theory of parallel lines, Translation, comments, introductory articles and notes by Professor V. F. Kagan. M.-L.: Publishing House of the USSR Academy of Sciences, 1945, 176 pp., djvu.

N. I. Lobachevsky. Geometric studies on the theory of parallel lines. 1941, pdf.

N. I. Lobachevsky. On the principles of geometry. (Part 1). Imaginary geometry. (1 part). New principles of geometry with a complete theory of parallels (Introduction).

On the foundations of geometry. A collection of classic works on Lobachevsky’s geometry and the development of its ideas. M.: Gostekhizdat, 1956.

Nikolai Ivanovich Lobachevsky - photo

Nikolai Ivanovich Lobachevsky - quotes

To live means to feel, to enjoy life, to constantly feel new things that would remind us that we are living.

A scientist must follow untrodden paths, despite obstacles.

Reason, without a doubt, belongs exclusively to man; intelligence means known beginnings judgments in which the first active causes of the universe seem to be imprinted and which thus agree all our conclusions with phenomena in nature, where contradictions cannot exist.

The first concepts with which any science begins must be clear and reduced to the smallest number. Then only they can serve as a solid and sufficient foundation for the teaching.

You can't be a genius if you weren't born. This is the art of educators: to discover genius, to enrich it with knowledge.

Nikolai Ivanovich Lobachevsky (1793-1856)

The great Russian geometer, creator of non-Euclidean geometry Nikolai Ivanovich Lobachevsky was born on November 2, 1793 in the Nizhny Novgorod province, into a poor family of a petty official. After a childhood filled with need and deprivation, after graduating from the gymnasium, which he managed to enter only thanks to the exceptional energy of his mother Praskovya Alexandrovna, we see him as a fourteen-year-old boy already a student at the newly opened Kazan University, within the walls of which all his further life and work take place. . N.I. Lobachevsky was lucky enough to study mathematics at the gymnasium with an extraordinary person and, apparently, a brilliant teacher - Grigory Ivanovich Kartashevsky. It was under his influence that the mathematical abilities of the future great geometer developed. As a student, he studied with the famous Bartels, a professor first at Kazan and then at Yuryev University, seriously mastering the mathematics of his time from primary sources, mainly from the works of Gauss and Laplace. However, despite the early manifested mathematical talents, N. I. Lobachevsky did not immediately decide to devote himself to mathematics; There is information that he initially prepared himself to practice medicine. In any case, by the age of 18 he had already chosen mathematics.

The student years of N. I. Lobachevsky were filled not only with an ardent passion for science and persistent scientific studies; they are full of youthful pranks and pranks, in which his cheerful character manifested itself very early. It is known that he was in a punishment cell for launching a rocket in Kazan at 11 pm, and that he was accused of many other mischiefs. But, besides this, more serious offenses are also noted: “free-thinking and dreamy self-conceit, perseverance” and even “outrageous actions..., which, to a large extent, showed signs of godlessness.”

For all this, N.I. Lobachevsky almost paid with expulsion from the university, and only the strong petitions of Kazan mathematics professors gave him the opportunity to graduate. His further career is developing rapidly: for 21 years N. I. Lobachevsky is an adjunct, and for 23 years he is an extraordinary professor; During these same years, in connection with the lectures on geometry that he gave in 1816-1817, he first approached the question, the solution of which was the glory of his life - the question of the axiom of parallels.

N.I. Lobachevsky’s youth was ending. The period of full disclosure of his rich and diverse personality began. Scientific creativity began, exceptional in its mathematical power. His amazingly multifaceted work, full of unyielding energy and passion, began and quickly developed as a professor, soon in all respects the first professor at Kazan University. His enthusiastic participation in all areas of activity, organization and construction of Kazan University began, which then turned into almost twenty years of complete and sole leadership of the entire university life. Just the enumeration of the various university positions he held successively, and often in parallel, gives an idea of the scope of his university work. At the end of 1819 he was elected dean; At the same time, he was given the responsibility of putting the university library in order, which was in an incredibly chaotic state. His professorial activity in these same years received new content: after the departure of Professor Simonov to trip around the world, as many as two academic year he has to read physics, meteorology and astronomy. By the way, N.I. Lobachevsky never lost interest in physics and did not refuse not only from teaching it at the university, but also from giving popular lectures on physics, accompanied by carefully and interestingly prepared experiments. In 1822 N.I. Lobachevsky became an ordinary professor; at the same time, he becomes a member of the construction committee for the renovation of old and construction of new university buildings. In 1825 he was already the chairman of this committee. In fact, he is the main builder of the entire set of new buildings at Kazan University and, fascinated by these new responsibilities, carefully studies architecture from both the engineering, technical and artistic sides. Many of the most architecturally successful buildings of Kazan University are the implementation of the construction plans of N. I. Lobachevsky; These are: anatomical theatre, library, observatory.

Finally, in 1827 N.I. Lobachevsky became rector of the university and held this post for 19 years. He understands his responsibilities as a rector very broadly: from ideological leadership of teaching and the entire life of the university to personal involvement in all everyday university needs. Having become rector, he continued to carry out the duties of the university librarian for several years and laid them down only after he had raised the library to the proper height. As an example of the energy and activity shown by N. I. Lobachevsky for the benefit of the university, it should be said about his role during two tragic events that befell Kazan life during his rectorship. The first of these events was the cholera epidemic of 1830, which raged in the Volga region and claimed many thousands of lives. When cholera reached Kazan, N. I. Lobachevsky immediately took heroic measures against the university: the university was virtually isolated from the rest of the city and turned, as it were, into a fortress. Accommodation and meals for students were organized on the university territory itself - all this with the active participation of the rector. The success was brilliant - the epidemic passed by the university. The energetic, selfless work of N. I. Lobachevsky in the fight against cholera made such a great impression on the entire society of that time that even official authorities considered it necessary to note it; N. I. Lobachevsky was expressed the “highest favor” for his diligence in protecting the university and other educational institutions from cholera.

Another disaster that struck Kazan was a fire, terrible in its devastating consequences, in 1842. During this terrible fire, which destroyed a huge part of the city, N. I. Lobachevsky again showed miracles of energy and stewardship in saving university property from the fire. In particular, he managed to preserve the library and astronomical instruments.

However, the central point of application of the energy and talents of N. I. Lobachevsky as the rector of the university was his direct concern for the education of youth in the broadest sense of the word. All other aspects of his activity as rector constituted only a framework for the implementation of this main task. The problems of education attracted him in all their scope and, like everything that interested him, they interested him in the most ardent way. Since 1818, N.I. Lobachevsky was a member of the school committee in charge of secondary and lower educational institutions, and since then he did not lose sight of, along with the issues of university teaching, the demands of school life. Constantly supervising entrance exams to the university, N. I. Lobachevsky knew perfectly well what knowledge a schoolchild of that time came to a higher educational institution with. Interested in the entire line of human development - from childhood to late adolescence - he demanded a lot from education, and the ideal of the human personality that was pictured before him was very high. N. I. Lobachevsky’s speech “On the Most Important Subjects of Education” is a remarkable monument not only to pedagogical thought, but, if I may put it this way, to that “educational emotion”, that pedagogical pathos, without which pedagogical activity itself turns into a deadening craft. N.I. Lobachevsky himself fully possessed the diversity and breadth of life interests that were part of his ideal of a harmoniously developed human personality. Naturally, he demanded a lot from young man who came to the university to study. He first of all demands from him that he be a citizen, “who with high knowledge constitutes the honor and glory of his fatherland,” that is, he sets before him a high and responsible patriotic ideal, based, in particular, on high qualifications within the chosen profession. But he further emphasizes that “mental education alone does not complete education,” and makes great demands on an intelligent person as a full-fledged representative of intellectual, ethical and aesthetic culture. N.I. Lobachevsky was not only an education theorist, but in fact an educator, a teacher of youth. He was not only a professor who delivered his lectures brilliantly and carefully, but also a man who knew the direct path to the youthful heart and knew how to find those very the right words who were able to act on a student who had gone astray, return him to work, and discipline him. The authority of N. I. Lobachevsky among students was extremely high. Students loved Nikolai Ivanovich, despite his severity as a professor and, in particular, as an examiner, despite his ardor and sometimes harshness.

N. I. Lobachevsky is probably the most big man, put forward by the almost two hundred years of glorious history of Russian universities. Even if he had not written a single line of independent scientific research, we would nevertheless have to remember him with gratitude as our most remarkable university figure, as a person who high ranks professor and rector of the university gave such completeness of content that none of the other persons who held these titles before him, during his time or after his death gave them. But N.I. Lobachevsky, in addition, was also a brilliant scientist, and if he had not been such, if he had not, along with all his other gifts, also had a first-class creative gift and creative experience, he would have been both in the field of university teaching and university leadership, and his very educational activities could not have been who he really was.

The main scientific merit of N. I. Lobachevsky lies in the fact that he was the first to fully understand the logical unprovability of the Euclidean axiom of parallels and drew all the main mathematical conclusions from this unprovability. The axiom of parallels, as is known, states: in a given plane to a given line, through a given point that does not lie on this line, one can draw only one parallel line. Unlike the other axioms of elementary geometry, the axiom of parallels does not have the property of immediate obviousness, if only because it is a statement about the entire infinite straight line as a whole, whereas in our experience we are faced only with larger or smaller “pieces” (segments ) straight. Therefore, throughout the history of geometry - from antiquity to the first quarter of the last century - there were attempts to prove the axiom of parallels, that is, to derive it from the other axioms of geometry. N.I. Lobachevsky also began with such attempts, accepting the assumption opposite to this axiom that to a given straight line through this point at least two parallel ones can be drawn. N.I. Lobachevsky sought to lead this assumption to a contradiction. However, as he developed an increasingly long chain of consequences from the assumption he made and the totality of the rest of Euclid’s axioms, it became increasingly clear to him that no contradiction not only did not arise, but could not result. Instead of a contradiction, N.I. Lobachevsky received, although unique, a logically completely harmonious and impeccable system of propositions, a system possessing the same logical perfection as ordinary Euclidean geometry. This system of propositions constitutes the so-called non-Euclidean geometry or Lobachevsky geometry.

Having received the conviction of the consistency of the geometric system he had constructed, N. I. Lobachevsky did not give a strict proof of this consistency, and could not give it, since such a proof went beyond the methods of mathematics early XIX V. The proof of the consistency of Lobachevsky's geometry was given only at the end of the last century by Cayley, Poincaré and Klein.

Without giving a formal proof of the logical equality of his geometric system with the usual system of Euclid, N. I. Lobachevsky essentially fully understood the indubitability of the very fact of this equality, expressing with complete certainty that given the logical impeccability of both geometric systems, the question of which of them is realized in physical world, can only be resolved by experience. N.I. Lobachevsky was the first to look at mathematics as an experimental science, and not as an abstract logical scheme. He was the first to conduct experiments to measure the sum of the angles of a triangle; the first who managed to abandon the thousand-year-old prejudice of the apriority of geometric truths. It is known that he loved to often repeat the words: “Stop working in vain, trying to extract all the wisdom from one mind, ask nature, it keeps all the secrets and will certainly answer your questions satisfactorily.” From the point of view of N. I. Lobachevsky modern science makes only one amendment. The question of what geometry is realized in the physical world does not have the immediate naive meaning that was given to it in the time of Lobachevsky. After all, the most basic concepts of geometry - the concepts of a point and a line, having been born, like all our knowledge, from experience, are, nevertheless, not directly given to us in experience, but arose only through abstraction from experience, as our idealizations of experimental data, idealization, which alone makes it possible to apply the mathematical method to the study of reality. To clarify this, we only point out that the geometric straight line, by virtue of its infinity alone, is not - in the form in which it is studied in geometry - the subject of our experience, but only an idealization of very long and thin rods or light rays that we directly perceive . Therefore, a final experimental verification of the parallel axiom of Euclid or Lobachevsky is impossible, just as an absolutely accurate determination of the sum of the angles of a triangle is impossible: all measurements of any physical angles given to us are always only approximate. We can only assert that Euclid’s geometry is an idealization of actual spatial relationships, which completely satisfies us as long as we are dealing with “pieces of space that are not very large and not very small,” that is, as long as we do not end up in either one or the other side too far beyond our usual, practical scale, while we, on the one hand, say, remain within solar system, and on the other hand, we do not dive too deep into the depths of the atomic nucleus.

The situation changes when we move to cosmic scales. The modern general theory of relativity considers the geometric structure of space as something dependent on the masses acting in this space and comes to the need to involve geometric systems that are “non-Euclidean” in a much more complex sense of the word than the one associated with Lobachevsky’s geometry.

The significance of the very fact of the creation of non-Euclidean geometry for all modern mathematics and natural science is colossal, and the English mathematician Clifford, who called N. I. Lobachevsky the “Copernicus of geometry,” did not fall into exaggeration. N.I. Lobachevsky destroyed the dogma of the “fixed, only true Euclidean geometry” in the same way as Copernicus destroyed the dogma of the stationary, constituting the unshakable center of the Universe - the Earth. N.I. Lobachevsky convincingly showed that our geometry is one of several logically equal geometries, equally impeccable, equally valuable logically, equally true in quality mathematical theories. The question is which of these theories is true in the physical sense of the word, that is, most suitable for the study of a particular circle physical phenomena, is precisely a question of physics, and not mathematics, and, moreover, a question the solution of which is not given once and for all by Euclidean geometry, but depends on the range of physical phenomena we have chosen. The only, albeit significant, privilege of Euclidean geometry remains that it continues to be a mathematical idealization of our everyday spatial experience and therefore, of course, retains its basic position both in a significant part of mechanics and physics, and, moreover, in all technology. But this circumstance, of course, cannot diminish the philosophical and mathematical significance of N. I. Lobachevsky’s discovery.

These are, in brief, the main lines of the versatile cultural activities of Nikolai Ivanovich Lobachevsky. It remains to say a few more words about recent years his life. If the 20s and 30s of the XIX century. were a period of highest flourishing of both creative and scientific-pedagogical and organizational activities N.I. Lobachevsky, then from the mid-forties and, moreover, quite suddenly for N.I. Lobachevsky, a period of inaction and senile burnout begins. The main event that brought with it this tragic turning point in the life of N.I. Lobachevsky was his dismissal on August 14, 1846 from the post of rector. This dismissal occurred without the desire of N.I. Lobachevsky and contrary to the petition of the university council. Almost simultaneously, his dismissal from the post of professor of mathematics occurred, so that from the spring of 1847 N. I. Lobachevsky found himself removed from virtually all his duties at the university. This suspension had all the features of a gross official disqualification, bordering on direct insult.

It is quite understandable that N.I. Lobachevsky, for whom his work at the university was a large and irreplaceable part of his life, perceived his resignation as a heavy, irreparable blow. This blow was especially hard, of course, because it broke out at that time in N.I. Lobachevsky’s life, when his creative scientific work was basically completed and, therefore, university activities became the main content of his life. If we add to this the exceptionally active character of N. I. Lobachevsky and his habit, created over decades, of being a leader in organizational affairs, and not an ordinary participant, a habit to which he truly had the right, then the extent of the catastrophe that befell him will become quite clear. Personal sorrows filled the cup: the beloved son of N.I. Lobachevsky, an adult young man, died, according to contemporaries, very similar to his father in both appearance and character. N.I. Lobachevsky was never able to cope with this blow. Old age began - premature, but all the more depressing, with increasing signs of paradoxically early decrepitness. His health was rapidly declining. He began to lose his sight and by the end of his life he was completely blind. The last work, “Pangeometry,” was already dictated by him. Broken by life, a sick, blind old man, he died on February 24, 1856.

As a scientist, N.I. Lobachevsky is, in the full sense of the word, a revolutionary in science. For the first time, having broken through the idea of Euclidean geometry as the only conceivable system of geometric knowledge, the only conceivable set of proposals about spatial forms, N.I. Lobachevsky did not find not only recognition, but even a simple understanding of his ideas. It took half a century for these ideas to enter mathematical science and become integral to it. integral part and were the turning point that largely determined the entire style of mathematical thinking of the subsequent era and from which, in fact, Russian mathematics began. Therefore, during his lifetime, N.I. Lobachevsky found himself in the difficult position of an “unrecognized scientist.” But this lack of recognition did not break his spirit. He found a way out in the varied, vigorous activity that is briefly outlined above. The strength of Lobachevsky’s personality triumphed not only over all the difficulties of the dark time in which he lived, it also triumphed over what may be the most difficult thing for a scientist to survive: over ideological isolation, over a complete misunderstanding of what was dearest and most necessary to him - his scientific discoveries and ideas. However, one should not blame his contemporaries, among whom were prominent scientists, for not understanding Lobachevsky. His ideas were far ahead of his time. Of the foreign mathematicians, only the famous Gauss understood these ideas. But, having owned them, Gauss never had the courage to publicly declare it. However, he understood and appreciated Lobachevsky. He took the initiative in the only scientific honor that fell to Lobachevsky: at the suggestion of Gauss, Lobachevsky was elected in 1842 as a corresponding member of the Gottingen Royal Society of Sciences.

If N. I. Lobachevsky undoubtedly won the right to immortality in the history of science with his geometric works, then we should not forget that in other areas of mathematics he published a number of brilliant works on mathematical analysis, algebra and probability theory, as well as mechanics, physics and astronomy.

The name of N.I. Lobachevsky entered the treasury of world science. But the brilliant scientist always felt like a fighter for Russian national culture, an everyday builder of it, living by its interests, caring for its needs.

The main works of N. I. Lobachevsky: Complete works on geometry, Kazan, 1833, vol. I (contains: On the principles of geometry, 1829; Imaginary geometry, 1835; Application of imaginary geometry to certain integrals, 1836; New principles of geometry with the complete theory of parallels, 1835-1838); 1886, vol. II (contains writings on foreign languages, including: Geometrische Untersuchungen zur Theorie der Parallellinien, 1840, in which N. I. Lobachevsky outlined his ideas about non-Euclidean geometry); Geometric research on the theory of parallel lines (Russian translation by A. V. Letnikov of the famous memoir of N. I. Lobachevsky Geometrische Untersuchungen...), "Mathematical collection", M., 1868, III; Pangeometry, "Scientific Notes of Kazan University", 1855; Complete works, M. - L., Gostekhizdat, 1946.

About N. I. Lobachevsky:Yanishevsky E., Historical note about the life and work of N. I. Lobachevsky, Kazan, 1868; Vasiliev A. V., Nikolai Ivanovich Lobachevsky, St. Petersburg, 1914; Sintsov D. M., Nikolai Ivanovich Lobachevsky, Kharkov, 1941; Nikolai Ivanovich Lobachevsky (to the 150th anniversary of his birth; articles by P. S. Aleksandrov and A. N. Kolmogorov), M. - L., 1943; Nikolai Ivanovich Lobachevsky (articles by B. L. Laptev, P. A. Shirokov, N. G. Chebotarev), ed. Academy of Sciences of the USSR, M. - L., 1943; Kagan V.F., The great scientist N.I. Lobachevsky and his place in world science, M. - L., 1943; by him, N.I. Lobachevsky, ed. Academy of Sciences of the USSR, M. -L., 1944.

Nikolai Ivanovich Lobachevsky is a famous Russian scientist and mathematician. Born in November 20 (December 1), 1792.

His father, Ivan Lobachevsky, was a minor official. Mother - Praskovya Alexandrovna. Nikolai's father died early and, at the age of nine, he, along with his mother and brothers, moved to.

In a new city, he and his two brothers go to study at the local gymnasium. At the Kazan gymnasium, he shows great interest in mathematics. His teacher was Kartashevsky, a wonderful teacher, a graduate of Moscow State University.

In 1807 Nikolai Lobachevsky became a student. In higher educational institution teachers discovered that he had a remarkable ability to study physical and mathematical sciences.

In 1811 he graduated from the university and received a master's degree. His scientific activity did not end there; the University hired the talented graduate.

Lobachevsky was an ideological man and approached his work with great enthusiasm. At his Kazan University, he taught several sciences: physics, mathematics and astronomy.

For more fruitful activities and development of the University, Lobachevsky purchased special equipment for physical experiments.

Through his efforts, books were purchased to update the University Library. Later, Nikolai Ivanovich was elected several times as dean of the Faculty of Physics and Mathematics. The scientist also headed the observatory and library.

In 1827, Lobachevsky was elected rector. With his characteristic enthusiasm, he accepted the appointment. Between 1832 and 1840, it was built large number various buildings intended for scientific activities.

New library, astronomical observatory, chemistry room, laboratories. The university was developing. The level of knowledge of students has increased greatly, and the teaching staff has been updated for the better. The position of rector did not separate Lobachevsky from his scientific activities. Nikolai Ivanovich continued to lecture at the University. The students highly valued their teacher.

Over the years of his scientific activity, Nikolai Lobachevsky has made a number of interesting discoveries in the field of mathematics. He developed a method for approximate solution of equations, derived a number of theorems on trigonometric series, also gave the most complete concept of a continuous function, and made a huge contribution to the development of non-Euclidean geometry.

Unfortunately, Nikolai Lobachevsky belonged to that number of geniuses who were not recognized in life. His discoveries were treated with great skepticism. However, over time, the works of the Russian scientist were recognized by the domestic and world scientific community.

His works were recognized thanks to the research of such foreign scientists as Beltrami, Klein, Poincaré. For the centenary of the Great, a monument to Lobachevsky was erected in Kazan.

Nikolai Ivanovich died on February 12 (02/24), 1856.

In 1792, Nikolai Ivanovich Lobachevsky was born in Nizhny Novgorod. At the age of nine Nikolay Lobachevsky he and his family move to Kazan, where he is enrolled in a gymnasium at “public expense.” In 1807, 14-year-old Nikolai Lobachevsky entered the newly established Kazan University. The teaching staff of the university was unique. Among the mathematicians were such famous scientists as Professor Martin Fedorovich (Johann Martin Christian) Bartels, a close friend of Carl Gauss.

Nikolai Lobachevsky immediately attracted attention. Teachers spoke of Lobachevsky as a young man, well-informed and deeply versed in subtle issues. The dean of the university was confident that Lobachevsky “will not be able to remain unfamous in the future.” The inspection certified Nikolai Lobachevsky as “a stubborn, unrepentant young man who dreams a lot about himself,” even showing “signs of godlessness.” It was only thanks to the patronage of the professorial staff that Lobachevsky received his master's degree.

Unusual mathematical abilities and high ability to work allowed Lobachevsky to achieve great heights in his scientific career.

In 1814, Lobachevsky, at the request of Bartels, was approved as an adjunct (assistant professor). Two years later, at the age of 23, Nikolai Lobachevsky becomes an extraordinary professor (associate professor). In 1822, Lobachevsky received the title of ordinary professor.

Rapidly developing career at the university, numerous scientific discoveries and achievements made the name of Lobachevsky widely known outside the Fatherland.

During pedagogical activity Lobachevsky gave more than a dozen lecture courses: number theory (according to Gauss), plane and spherical trigonometry, analytical and descriptive geometry, astronomy, differential and integral calculus (physics, statics and dynamics, etc. It follows that the young professor lectured not only in various branches of mathematical science, but also in physics and astronomy.

Lobachevsky's active work as both a teacher and a scientist increases his authority. He is entrusted with the management of the observatory and appointed dean of the Faculty of Mathematics. For many years, Lobachevsky headed the university library. As chairman of the university's construction committee, he personally supervised the construction of new academic buildings.

In 1827, Lobachevsky was elected to the post of rector of Kazan University. He was later re-elected to this position six times and remained rector for 20 years. Energetic and active Lobachevsky was engaged in both academic and scientific work, strictly monitored finances and construction.

In 1846, Lobachevsky was removed from the post of rector.

Lobachevsky gained greatest fame thanks to the creation of non-Euclidean geometry. Since 1817, Lobachevsky has devoted himself to working on solving one of the most difficult geometric problems - proving Euclid's fifth postulate about parallel lines.

For many centuries, hundreds of mathematicians around the world have studied the problem of the fifth postulate, but their research was in vain. Lobachevsky approached this problem differently; he gave it special meaning. According to him, “the problem of parallels is a difficulty that has so far been invincible, but at the same time contains truths that are tangible, without any doubt, and so important for the purposes of science that they cannot be avoided.”

At the first stage of his research, Lobachevsky acted like most mathematicians, namely, he looked for proof by contradiction. However, this path did not lead to the desired results; the desired contradiction was never achieved.

Finally, in 1823, Lobachevsky came to the conclusion that Euclid’s fifth postulate was unprovable and it was possible to create a new geometry. In addition, Lobachevsky claims that the new geometry, despite the unusualness of its content, cannot be rejected by experience.

The first work devoted to the new geometry was written by Lobachevsky in February 1826. Unfortunately, university colleagues ignored Lobachevsky's discovery. This work was subsequently lost.

But even this unpleasant event did not stop Lobachevsky on the path to creating and proving the existence of a new non-Euclidean geometry.

In 1829, the Kazansky Vestnik magazine published a new work by Lobachevsky on non-Euclidean geometry. From Lobachevsky’s point of view, Euclid’s axiom is an arbitrary, too strict restriction that does not make it possible to fully describe the properties of space. As an alternative, Lobachevsky puts forward a new axiom: on a plane, through a point that does not lie on a given line, there passes more than one line that does not intersect the given one. Lobachevsky's new geometry does not include Euclidean geometry, however, Euclidean geometry can be obtained from it by passing to the limit (as the curvature of space tends to zero). Thus, the curvature in Lobachevsky geometry is negative.

Alas, Lobachevsky’s brilliant ideas were again not understood by his contemporaries.

A genius is always ahead of his time. Only 40 years later will Lobachevsky’s works be appreciated. Many scientists will devote dozens of works to proving the validity of Lobachevsky's geometry along with Euclid's geometry. However, this will happen later, and in the late 20s. In the 19th century, Lobachevsky was in a very difficult and ambiguous position.

Misunderstanding, ridicule, harsh condemnation, and sometimes insulting reviews were often addressed to Nikolai Lobachevsky. The brilliant scientist passed these tests with honor.

One of the first scientists who agreed with Lobachevsky’s work was the “king of mathematicians” - Carl Gauss. It was on his recommendation that Lobachevsky was invited to the position of corresponding member of the Gottingen Scientific Society (Academy of Sciences) in 1842.

Shortly before his death, Nikolai Ivanovich Lobachevsky completely loses his sight. Last job“Pangeometry,” dedicated to the 50th anniversary of Kazan University, he dictated to his students. In 1856, Nikolai Ivanovich Lobachevsky passed away. The creator of non-Euclidean geometry died unrecognized.

Decades later, thanks to researchers E. Beltram, F. Klein and A. Poincaré, the Lobachevsky geometry was proven.

A striking example of faithful service to the fatherland and science was the life of the great Russian mathematician Nikolai Ivanovich Lobachevsky.

Lobachevsky, Nikolai Ivanovich - creator of non-Euclidean geometry, Russian mathematician, rector of Kazan University.

Biography

Nikolai Ivanovich Lobachevsky was born on December 1, 1792 in Nizhny Novgorod. Father, Ivan Maksimovich Lobachevsky, served in the geodetic department. Mother, Praskovya Alexandrovna, raised three children and took care of the house.

In 1802, Nikolai was sent to the Kazan gymnasium, where he studied for four years in government pay. Demonstrated good knowledge of German, Latin, French, mathematics.

In 1806, Lobachevsky tried to join the newly created Kazan University, but failed. entrance exams. However, a few months later he repeated the attempt, which this time turned out to be successful. In 1807, Nikolai was officially enrolled in the university. At first he paid a lot of attention to medicine, but soon decided to focus on physical and mathematical sciences. In 1808 he was sent to punishment cell for his pyrotechnic experiments.

In 1811, Nikolai graduated from the university with a master's degree in mathematics and physics. He remains at the university and continues to engage in scientific activities.

In 1814, Lobachevsky began teaching at Kazan University. In 1816 he became an extraordinary professor. Teaches algebra, arithmetic, trigonometry.

In 1819, the university was visited by an auditor who was very unhappy with the state of the faculties. Everyone except physics and mathematics. Its dean, Bartels, left with other foreigners, and Lobachevsky was appointed dean. In 1824, the young dean was presented to the Order of St. Vladimir IV degree.

In 1826, immediately after the ascension to the throne of Nicholas I, trustee Magnitsky, who was at odds with Lobachevsky, was removed from his post. He is accused of abuses and tried in the Senate. The very next year Lobachevsky became rector of the university.

In this position, Nikolai Ivanovich established himself only with the best side. His list of concerns includes: construction of educational buildings, reorganization of the staff, maintenance of the library, development of the mineralogical collection, participation in the publication of the newspaper “Kazansky Vestnik” and much more. He teaches courses in trigonometry and geometry, algebra, probability theory, physics, mechanics, and astronomy. Independently replaced absent teachers.

All this time, Lobachevsky was actively working on the main work of his life - the creation of non-Euclidean geometry. On February 23, 1826, Lobachevsky gave a report “A condensed presentation of the principles of geometry.” Now this date is considered the birthday of non-Euclidean geometry.

In 1832 Nikolai Ivanovich got married. His wife was Varvara Alekseevna Moiseeva, who was 20 years younger than her husband. In the same year, in St. Petersburg, Lobachevsky's works on non-Euclidean geometry were sharply criticized. However, critics gradually calmed down. In 1836, Nicholas I personally awarded Lobachevsky the Order of Anna, II degree. After this, Nikolai Ivanovich automatically became a hereditary nobleman.

In 1845, Lobachevsky became a trustee of the Kazan educational district and was elected to the position of rector for the fourth time. The following year he was suspended from teaching for length of service.

Soon misfortunes began to haunt Lobachevsky. He went bankrupt; both his house and his wife’s estate were sold for debts. Son Andrei dies of tuberculosis. Nikolai Ivanovich’s health is also weakening, he is losing his sight. In 1855, he completed his last work, Pangeometry, which he dictated to his students.

On February 24, 1856, Nikolai Ivanovich Lobachevsky died. His body was buried at the Arskoye cemetery in Kazan.

Lobachevsky's main achievements

Lobachevsky's main achievements, of course, relate to geometry. He became the creator of non-Euclidean geometry. His ideas were supported by the then “king of mathematics” Gauss. Lobachevsky remained unrecognized by most of his contemporaries, but in the future his works were appreciated. Already in the second half of the 1860s, Lobachevsky’s works became popular in Russia and abroad, and beyond full meeting Kazan University wanted to receive 600 rubles for his works. Only 16 years later it was possible to collect the mathematician’s works, but some of them were lost and have not been discovered to this day.
Lobachevsky achieved significant results in other mathematical fields. He developed a new method for solving equations, created a number of theorems on trigonometric series, and studied continuous functions.
He published a number of remarkable articles on algebra and analysis, physics, mechanics, astronomy, and probability theory.

Important dates in Lobachevsky’s biography

December 1, 1792 - birth in Nizhny Novgorod.
1802 - admission to the Kazan gymnasium.
1806 – graduation from high school, admission to Kazan University.
1811 – graduation from the university with a master's degree. Publication of the argument “Theory of elliptic motion celestial bodies" Work at the university.
1814 - approval of pure mathematics by an adjunct. Start of teaching activity.
1816 - confirmation by an extraordinary professor.
1818 – Member of the District School Committee.
1820 – appointment as dean of the Faculty of Physics and Mathematics at Kazan University.
1824 - awarded the Order of St. Vladimir IV degree.
1826 – publication of the report “A Concise Exposition of the Principles of Geometry.” The birth of non-Euclidean geometry.
1827 – election as rector of the university.
1832 - marriage to Varvara Alekseevna Moiseeva.
1836 - awarded the Order of Anna II degree from the hands of Nicholas I.
1838 - Nobility granted.
1845 - appointment as trustee of the St. Petersburg educational district.
1846 – death of daughter Nadezhda. Removal from the position of rector and professorship.
1855 – completion of work on the last work “Pangeometry”.
February 24, 1856 - died at home after illness.

In the gymnasium he was fond of pyrotechnic experiments, for which he ended up in a punishment cell. The teachers did not like him for his freethinking and perseverance.
He became a master at the age of 19, and a professor at the age of 24.
He loved to garden. His “favorites” in the garden were cedars. Lobachevsky said that he would not wait to see their fruits. They were filmed just a few months after the scientist's death.
Lobachevsky was afraid that his works would be forgotten after his death. These fears were fueled by intense criticism of his work.
In 1992, the Lobachevsky medal was established. It is issued every five years for outstanding achievements in the study of geometry.
Lobachevsky had every chance of getting into the army when a decree was issued ordering those students who were distinguished by bad behavior to be sent to the service.
While studying at the university, he often showed disrespect for religion, which he was forgiven for only for his brilliant knowledge of mathematics.
Actively introduced all kinds of innovations in agriculture. He even received awards for some achievements in this field.
He had a remarkable gift of persuasion. Lobachevsky calmed one of his students, who loved to drink and even rushed at people with a knife, only with a calm conversation.
He loved to have fun with students, but he never allowed familiarity.